A System of Geometry and Trigonometry, with a Treatise on Surveying: In which the Principles of Rectangular Surveying Without Plotting are Explained

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Belknap and Hamersley, 1837 - Geometry - 272 pages
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Page 10 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes; and each minute into 60 equal parts, called seconds ; and these into thirds, &c . NOTE.
Page 34 - As the base or sum of the segments Is to the sum of the other two sides, So is the difference of those sides To the difference of the segments of the base.
Page 34 - Plane Triangle, As the Sum of any two Sides ; Is to their Difference ; So is the Tangent of half the Sum of the two opposite Angles ; To the Tangent of half the Difference between them.
Page 30 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Page 50 - OF PROTRACTING FIELDS. Without drawing parallel lines at the end of each side, a field may be protracted by the angles made by the several sides ; and the angle made between any two sides may be found by the following RULES. RULE 1. If the course or bearing of one of the sides is north and the other south, one east and the other west, subtract the less course from the greater.
Page 25 - ADD the logarithms of the SECOND and THIRD terms, and .from the sum SUBTRACT the logarithm of the FIRST term. The remainder will be the logarithm of the term required.
Page 9 - NB The minutes in the left-hand column of each page, increasing downwards, belong to the degrees at the top ; and those increasing upwards, in the right-hand column, belong to the degrees below.
Page 10 - The radius of a circle is a line drawn from the centre to the circumference, as A, B.
Page 12 - Fig. 7, that the sine of any arc is the same as that of its supplement. So likewise, the tangent and secant of any arc are used also for its supplement.] 27.
Page 159 - O's, points or dots are introduced instead of the O's through the rest of the line, to catch the eye, and to indicate that from thence the annexed first two figures of the Logarithm in the second column stand in the next lower line. N.

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